You should be fine with a 23, but you should also be aware that (if I understood you correctly) the tire you are considering is a passenger car tire that is also approved for light truck service. Presumably it is a P235/75-15 LTX MS/2, but not an LT235 tire, as the last time I looked Michelin did not make LT (Light Truck) tires in a 15" size. The point of all this is that these tires, when used in trailer service, should be de-rated to 90% of the published rating. Many on here run those tires, even on 25 and larger trailers and have reported good results. I chose not to use them on my 25 because the weight carrying capacity was not close to that provided by the tires specified for my trailer.
"You cannot reason someone out of a position they have not been reasoned into"
Al, K5TAN and Missy, N4RGO
2002 Classic 30 Slideout
2001 Safari 25 RB Twin (Gone, but not forgotten)
2013 Dodge 2500 Laramie 4x4 Megacab Cummins
WBCCI 1322, TAC FL-39, AIR 82265